Deck of Cards Probability Explained

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Deck of cards probability
Deck of Cards Probability Explained

Many questions come up in probability involving a deck of playing cards.  Furthermore, many times card players will also want to know different probabilities for the card games they are involved in.

In this post, you will learn about probability with a deck of cards and how it works.  This will include examples of probability with cards, and also how many ways a deck of cards can be shuffled and arranged.  Finally, common playing card probability questions will be answered.

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How a Deck of Cards Works

If you need to learn how a deck of cards works, you can watch the video below.

Or, for a more detailed guide on how a deck works, you can visit 52 Playing Cards Details.

Probability Intro to a Standard Deck of Cards

52 Playing Cards Details

Just for a quick reference, here are some numbers that are important to know about a deck of cards when doing probability.

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See also  How Many Red Face Cards are in a Deck of 52 Cards?

How Are 52 Cards Divided?

The 52 cards in the deck are divided into 4 suits. These suits are the Hearts, Diamonds, Clubs and Spades. The Hearts and Diamonds are the red suits. The Clubs and Spades are the black suits.

Each suit has the same 13 value cards. These cards are the Ace, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Jack, Queen, and King.

(Learn more at Types of Cards in a Deck of 52 Cards)

How Many Cards in a Deck?

There are 52 cards in a full deck of cards, not including the Jokers. If you include the 2 Jokers, then there are 54 cards in a deck.

In probability, a deck of cards is 52 cards. (The Jokers are not included)

How Many Face Cards In a Deck?

There are 12 face cards in a deck. Each of the 4 suits gets one of each of the 3 face cards, the Jack, Queen and King. There are 6 red face cards and 6 black face cards in a deck.

Full Deck of Cards

A full deck of cards will have 13 cards in each of the 4 suits. These 13 cards are the Ace, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Jack, Queen and King.

Here is an image of a full deck of cards with each of the 13 cards in each of the 4 suits.

Full deck of cards
Full deck of cards

Playing Cards Probability

Let’s look at an introduction to probability with playing cards.  This will give us a basic overview of the way probability works with playing cards.

Probability of a Regular Pack of 52 Cards Explained – Playing Cards Probability

Probability Examples with Cards

Next, we can look at some examples of probability with cards.

Probability Examples with Cards

We can also look at some probability examples using Venn Diagrams for more clarity.

Probability with playing cards and Venn diagrams

Face Cards in Probability

There are 12 face cards in a deck of 52 cards. This means that the odds of drawing a face card will be 12/52, or 3/13.

See also  Is an Ace a Face Card? Or is an Ace a Number Card?

The odds of drawing a non-face card will be the opposite of this, or 40/52, which simplifies to 10/13.

There are 6 red face cards and 6 black face cards in a deck. This means the odds of drawing a red face card are 6/52 or 3/26. The odds of drawing a black face card are the same, 3/26.

Shuffled Deck of Cards Probability

How Many Ways Can You Arrange a Deck?

How many ways can you shuffle a deck of cards? It’s hard to imagine, but if you shuffle a deck of cards, you are almost certainly holding a deck of cards that is in an order that has never been seen before in all history!

How many ways can you arrange a deck of cards?  There are exactly 8.07×10^67 ways that a 52 card deck can be arranged.

If this were written out, it would be the number 8 followed by 67 zeros!

How Many Ways Can You Order a Deck of Cards

See how mind-boggling this number actually is in the following video.

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Combinations of 52 Cards

Deck of Cards Probability Questions

What is the probability of drawing any card from a deck of cards?

The probability of drawing any random card from a deck of cards would be 1/52.

This is because you have 1 card that you can choose out of 52 options.

What is the probability of drawing an Ace from a deck of cards?

The probability of drawing an Ace from a deck of cards is 1/13.

This is because there are 4 Aces, and you have 52 total possible cards that could be drawn.

This gives you 4/52 as the probability of drawing an Ace, which is simplified to 1/13.

What is the probability of drawing a red card from a deck of cards?

The probability of drawing a red card from a deck is 1/2.

This is because there are 26 red cards out of 52 possible choices.

This gives 26 chances of selecting a red card out of 52, or 26/52.  This simplifies to 1/2.

What is the probability of drawing a black card from a deck of cards?

The probability of drawing a black card from a deck is 1/2.

This is because there are 26 black cards out of 52 possible choices.

This gives 26 chances of selecting a black card out of 52, or 26/52.  This simplifies to 1/2.

What is the probability of drawing a Heart from a deck of cards?

The probability of drawing a Heart from a deck of cards is 1/4.

This is because there are 13 Heart cards in a deck out of 52 possible cards.

This gives 13 chances to select a Heart out of 52 possible cards.  This gives a probability of 13/52.  This simplifies to 1/4.

What is the probability of drawing a Diamond from a deck of cards?

The probability of drawing a Heart from a deck of cards is 1/4.

This is because there are 13 Diamond cards in a deck out of 52 possible cards.

This gives 13 chances to select a Diamond out of 52 possible cards.  This gives a probability of 13/52.  This simplifies to 1/4.

See also  How Many Hearts are in a Deck of Cards of 52?

What is the probability of drawing a Spade from a deck of cards?

The probability of drawing a Heart from a deck of cards is 1/4.

This is because there are 13 Spade cards in a deck out of 52 possible cards.

This gives 13 chances to select a Spade out of 52 possible cards.  This gives a probability of 13/52.  This simplifies to 1/4.

What is the probability of drawing a Club from a deck of cards?

The probability of drawing a Heart from a deck of cards is 1/4.

This is because there are 13 Club cards in a deck out of 52 possible cards.

This gives 13 chances to select a Club out of 52 possible cards.  This gives a probability of 13/52.  This simplifies to 1/4.

What is the probability of drawing a face card from a deck of cards?

The probability of drawing a face card from a deck of cards is 3/13.

This is because there are 12 face cards in a deck out of 52 total cards.  This gives 12 changes to draw a face card out of 52 possibilities.

This means the chance of getting a face card is 12/52.  This simplifies to 3/13.

What is the probability of drawing a King from a deck of cards?

The probability of drawing a King from a deck of cards is 1/13.

This is because there are 4 Kings, and you have 52 total possible cards that could be drawn.

This gives you 4/52 as the probability of drawing a King, which is simplified to 1/13.

What is the probability of drawing a Queen from a deck of cards?

The probability of drawing a Queen from a deck of cards is 1/13.

This is because there are 4 Queens, and you have 52 total possible cards that could be drawn.

This gives you 4/52 as the probability of drawing a Queen, which is simplified to 1/13.

What is the probability of drawing a Queen from a deck of cards?

The probability of drawing a Jack from a deck of cards is 1/13.

This is because there are 4 Jacks, and you have 52 total possible cards that could be drawn.

This gives you 4/52 as the probability of drawing a Jack, which is simplified to 1/13.

What is the Probability of Getting a Non-Face Card in a Deck of Cards?

The probability of getting a non-face card from a deck of 52 cards, would be 40/52, or 10/13.

This is because there are 40 non-face cards that can be possibly chosen, out of a total of 52 cards.

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